Question

question 11 (3 points)
find m∠1, m∠2 and m∠3. complete the reasoning:
m∠1 =
° is a
angle with the given.
m∠2 =
° is a corresponding angle with ∠1
m∠3 =
° is a vertical angle with ∠2
blank 1: 100
blank 2: 100
blank 3: 100
blank 4: corresponding
blank 5: 100
blank 6: vertical

Explanation:

Step1: Identify supplementary angle

Since the angle adjacent to ∠1 is 80°, and a straight - line angle is 180°, then $m\angle1=180 - 80=100^{\circ}$.

Step2: Use corresponding - angle property

Parallel lines are given (by the arrow marks). Corresponding angles are equal. Since ∠2 is corresponding to ∠1, $m\angle2 = m\angle1=100^{\circ}$.

Step3: Use vertical - angle property

Vertical angles are equal. Since ∠3 is vertical to ∠2, $m\angle3 = m\angle2=100^{\circ}$.

Answer:

$m\angle1 = 100^{\circ}$, $m\angle2 = 100^{\circ}$, $m\angle3 = 100^{\circ}$